How to express fractions as decimals

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How to express fractions as decimals or percentage

This post will help you to learn:

Express a given percent as a decimal or fraction.

Solve a given problem that involves finding a percent.

Determine the answer to a given percent problem where the answer requires rounding, and explain why an approximate answer is needed (e.g., total cost including taxes).

Work problems involving pie charts and percents.

Work problems involving tables and percents.

Decimal Equivalents of Fractions

You should know these:

1/2 = .5 = 50%

1/3 = .333… = 33.33%

1/4 = .25 = 25%

Starting with the thirds, of which you already know one:

1/3 = .333… = 33.33%

2/3 = .666… = 66.66%

You also know 2 of the 4ths, as well, so there’s only one new one to learn:

1/4 = .25

2/4 = 1/2 = .5

3/4 = .75

Fifths are very easy. Take the numerator (the number on top), double it, and stick a

decimal in front of it.

1/5 = .2

2/5 = .4

3/5 = .6

4/5 = .8

There are only two new decimal equivalents to learn with the 6ths:

1/6 = .1666…

2/6 = 1/3 = .333…

3/6 = 1/2 = .5

4/6 = 2/3 = .666…

5/6 = .8333…

One-seventh is an interesting number. Read the comments on Cyclic Numbers

1/7 = .142857142857142857…

For now, just think of one-seventh as: 0.142857

See if you notice any pattern in the 7ths:

1/7 = .142857…

2/7 = .285714…

3/7 = .428571…

4/7 = .571428…

5/7 = .714285…

6/7 = .857142…

Notice that the 6 digits in the 7ths ALWAYS stay in the same order and the starting digit is the only thing that changes.

If you know your multiples of 14 up to 6, it isn’t difficult to work out where to begin the decimal number. Look at this:

For 1/7, think “1 * 14”, giving us .14 as the starting point.

For 2/7, think “2 * 14”, giving us .28 as the starting point.

For 3/7, think “3 * 14”, giving us .42 as the starting point.

For 4/14, 5/14 and 6/14, you’ll have to adjust upward by 1:

For 4/7, think “(4 * 14) + 1”, giving us .57 as the starting point.

For 5/7, think “(5 * 14) + 1”, giving us .71 as the starting point.

For 6/7, think “(6 * 14) + 1”, giving us .85 as the starting point.

8ths aren’t that hard to learn, as they’re just smaller steps than 4ths. If you have trouble

with any of the 8ths, find the nearest 4th, and add .125 if needed:

1/8 = .125

2/8 = 1/4 = .25

3/8 = .375

4/8 = 1/2 = .5

5/8 = .625

6/8 = 3/4 = .75

7/8 = .875

9ths are almost too easy:

1/9 = .111…

2/9 = .222…

….

8/9 = .888…

10ths are very easy, as well. Just put a decimal in front of the numerator:

1/10 = .1

2/10 = .2

…

9/10 = .9

Remember how easy 9ths were? 11th are easy in a similar way, assuming you know your multiples of 9:

1/11 = .090909… = 9.09%

2/11 = .181818… = 18.18%

3/11 = .272727… = 27.27%

…..

10/11 = .909090…

As long as you can remember the pattern for each fraction, it is quite simple to work out

the decimal place as far as you want or need to go!

Lesson Summary

In this lesson, the learner has learnt about:

The decimal equivalents of everything from 1/2 to 10/11Author: Vineet Patawari

Proper fractions with 9,99,999 etc as denominators yield repeating decimals if the number of digits is same in numerator and denominator. And the repeating decimals are the same as the numerator digits.
ex: 7/9 = 0.777777…
56/99 = 0.5656565656…
823/999 = 0.823823823823…
1426/9999 = 0.142614261426…
and so on.